ArticleOriginal scientific text

Title

On fuzzy ideals of pseudo MV-algebras

Authors 1

Affiliations

  1. Institute of Mathematics and Physics, University of Podlasie, 3 Maja 54, 08-110 Siedlce, Poland

Abstract

Fuzzy ideals of pseudo MV-algebras are investigated. The homomorphic properties of fuzzy prime ideals are given. A one-to-one correspondence between the set of maximal ideals and the set of fuzzy maximal ideals μ satisfying μ(0) = 1 and μ(1) = 0 is obtained.

Keywords

pseudo MV-algebra, fuzzy (prime, maximal) ideal

Bibliography

  1. C.C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490.
  2. A. Dvurečenskij, States on pseudo MV-algebras, Studia Logica 68 (2001), 301-327.
  3. G. Dymek, Fuzzy maximal ideals of pseudo MV-algebras, Comment. Math. 47 (2007), 31-46.
  4. G. Dymek, Fuzzy prime ideals of pseudo-MV algebras, Soft Comput. 12 (2008), 365-372.
  5. G. Georgescu and A. Iorgulescu, Pseudo MV-algebras: a non-commutative extension of MV-algebras, pp. 961-968 in: 'Proceedings of the Fourth International Symposium on Economic Informatics', Bucharest, Romania, May 1999.
  6. G. Georgescu and A. Iorgulescu, Pseudo MV-algebras, Multi. Val. Logic 6 (2001), 95-135.
  7. C.S. Hoo and S. Sessa, Fuzzy maximal ideals of BCI and MV-algebras, Inform. Sci. 80 (1994), 299-309.
  8. Y.B. Jun and A. Walendziak, Fuzzy ideals of pseudo MV-algebras, Inter. Rev. Fuzzy Math.~ 1 (2006), 21-31.
  9. J. Rachůnek, A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255-273.
  10. L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353.
Pages:
63-75
Main language of publication
English
Received
2007-02-23
Accepted
2007-04-04
Published
2008
Exact and natural sciences